Sliding Mode Control for Stochastic Jump Systems with Time-Delay

The problems of stochastic stability and sliding mode control for a class of linear time-delay systems with stochastic jumps are considered in this paper. The jumping parameters appeared in the system matrices are modelled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. Sufficient conditions are proposed to guarantee the stochastic stability of the underlying system based on linear matrix inequalities (LMI) approach. Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions.